Generalised Weyl theorems and spectral pollution in the Galerkin method
Generalised Weyl theorems and spectral pollution in the Galerkin method
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广义韦尔定理和伽辽金方法中的光谱污染
DOI：
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发表时间：
2010
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通讯作者：
Mathieu Lewin
中科院分区：
文献类型：
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作者：
L. Boulton;N. Boussaid;Mathieu Lewin
我们考虑一个一般的框架调查光谱污染的Galerkin方法。我们展示了这种现象的特点是通过存在特定的外尔序列是奇异的在一个合适的意义上。对于半有界自伴算子A，我们确定了自伴扰动B的相对紧性条件，保证了A和B的谱污染极限集重合。我们的结果表明，在扰动下，这个限制集的行为在一个类似的方式作为本质谱。
We consider a general framework for investigating spectral pollution in the Galerkin method. We show how this phenomenon is characterised via the existence of particular Weyl sequences which are singular in a suitable sense. For a semi-bounded selfadjoint operator A we identify relative compactness conditions on a selfadjoint perturbation B ensuring that the limiting set of spectral pollution of A and B coincide. Our results show that, under perturbation, this limiting set behaves in a similar fashion as the essential spectrum.